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In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets. If asset prices do not change in perfect synchrony, a diversified portfolio will have less variance than the weighted average variance of its constituent assets, and often less volatility than the least volatile of its constituents.^[1]

Diversification is one of two general techniques for reducing investment risk. The other is hedging.

Examples

The simplest example of diversification is provided by the proverb "Don't put all your eggs in one basket". Dropping the basket will break all the eggs. Placing each egg in a different basket is more diversified. There is more risk of losing one egg, but less risk of losing all of them. On the other hand, having a lot of baskets may increase costs.

In finance, an example of an undiversified portfolio is to hold only one stock. This is risky; it is not unusual for a single stock to go down 50% in one year. It is less common for a portfolio of 20 stocks to go down that much, especially if they are selected at random. If the stocks are selected from a variety of industries, company sizes and asset types it is even less likely to experience a 50% drop since it will mitigate any trends in that industry, company class, or asset type.

Since the mid-1970s, it has also been argued that geographic diversification would generate superior risk-adjusted returns for large institutional investors by reducing overall portfolio risk while capturing some of the higher rates of return offered by the emerging markets of Asia and Latin America.^[2][3]

Return expectations while diversifying

If the prior expectations of the returns on all assets in the portfolio are identical, the expected return on a diversified portfolio will be identical to that on an undiversified portfolio. Some assets will do better than others; but since one does not know in advance which assets will perform better, this fact cannot be exploited in advance. The return on a diversified portfolio can never exceed that of the top-performing investment, and indeed will always be lower than the highest return (unless all returns are identical). Conversely, the diversified portfolio's return will always be higher than that of the worst-performing investment. So by diversifying, one loses the chance of having invested solely in the single asset that comes out best, but one also avoids having invested solely in the asset that comes out worst. That is the role of diversification: it narrows the range of possible outcomes. Diversification need not either help or hurt expected returns, unless the alternative non-diversified portfolio has a higher expected return.^[4]

Amount of diversification

There is no magic number of stocks that is diversified versus not. Sometimes quoted is 30, although it can be as low as 10, provided they are carefully chosen. This is based on a result from John Evans and Stephen Archer.^[5] Similarly, a 1985 book reported that most value from diversification comes from the first 15 or 20 different stocks in a portfolio.^[6] More stocks give lower price volatility.

Given the advantages of diversification, many experts ^[who?] recommend maximum diversification, also known as "buying the market portfolio". Identifying that portfolio is not straightforward. The earliest definition comes from the capital asset pricing model which argues the maximum diversification comes from buying a pro rata share of all available assets. This is the idea underlying index funds.

Diversification has no maximum so long as more assets are available.^[7] Every equally weighted, uncorrelated asset added to a portfolio can add to that portfolio's measured diversification. When assets are not uniformly uncorrelated, a weighting approach that puts assets in proportion to their relative correlation can maximize the available diversification.

"Risk parity" is an alternative idea. This weights assets in inverse proportion to risk, so the portfolio has equal risk in all asset classes. This is justified both on theoretical grounds, and with the pragmatic argument that future risk is much easier to forecast than either future market price or future economic footprint.^[8] "Correlation parity" is an extension of risk parity, and is the solution whereby each asset in a portfolio has an equal correlation with the portfolio, and is therefore the "most diversified portfolio". Risk parity is the special case of correlation parity when all pair-wise correlations are equal.^[9]

Effect of diversification on variance

One simple measure of financial risk is variance of the return on the portfolio. Diversification can lower the variance of a portfolio's return below what it would be if the entire portfolio were invested in the asset with the lowest variance of return, even if the assets' returns are uncorrelated. For example, let asset X have stochastic return ${\displaystyle x}$ and asset Y have stochastic return ${\displaystyle y}$, with respective return variances ${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$. If the fraction ${\displaystyle q}$ of a one-unit (e.g. one-million-dollar) portfolio is placed in asset X and the fraction ${\displaystyle 1-q}$ is placed in Y, the stochastic portfolio return is ${\displaystyle qx+(1-q)y}$. If ${\displaystyle x}$ and ${\displaystyle y}$ are uncorrelated, the variance of portfolio return is ${\displaystyle {\text{var}}(qx+(1-q)y)=q^{2}\sigma _{x}^{2}+(1-q)^{2}\sigma _{y}^{2}}$. The variance-minimizing value of ${\displaystyle q}$ is ${\displaystyle q=\sigma _{y}^{2}/}$, which is strictly between ${\displaystyle 0}$ and ${\displaystyle 1}$. Using this value of ${\displaystyle q}$ in the expression for the variance of portfolio return gives the latter as ${\displaystyle \sigma _{x}^{2}\sigma _{y}^{2}/}$, which is less than what it would be at either of the undiversified values ${\displaystyle q=1}$ and ${\displaystyle q=0}$ (which respectively give portfolio return variance of ${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$). Note that the favorable effect of diversification on portfolio variance would be enhanced if ${\displaystyle x}$ and ${\displaystyle y}$ were negatively correlated but diminished (though not eliminated) if they were positively correlated.

In general, the presence of more assets in a portfolio leads to greater diversification benefits, as can be seen by considering portfolio variance as a function of ${\displaystyle n}$, the number of assets. For example, if all assets' returns are mutually uncorrelated and have identical variances ${\displaystyle \sigma _{x}^{2}}$, portfolio variance is minimized by holding all assets in the equal proportions ${\displaystyle 1/n}$.^[10] Then the portfolio return's variance equals ${\displaystyle {\text{var}}}$ = ${\displaystyle n(1/n^{2})\sigma _{x}^{2}}$ = ${\displaystyle \sigma _{x}^{2}/n}$, which is monotonically decreasing in ${\displaystyle n}$.

The latter analysis can be adapted to show why adding uncorrelated volatile assets to a portfolio,^[11][12] thereby increasing the portfolio's size, is not diversification, which involves subdividing the portfolio among many smaller investments. In the case of adding investments, the portfolio's return is ${\displaystyle x_1+x_2}$Zdroj:https://en.wikipedia.org?pojem=Diversification_(finance)
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